Large Deformation Of Free Surface Research Articles

Simulation of fallpipe rock dumping utilizing a multi-phase particle-in-cell (MPPIC)-Discrete Element Method (DEM) model. Part I: Concepts and formulation

Dumping blasted rock fragments into water bodies through vertical fallpipes can be a challenging engineering activity due to the concerns of dispersion of fine contents (suspended sediments). This study aims to provide better understanding of the fallpipe rock dumping processes through numerical simulation approaches. We propose a modified multiphase particle-in-cell (MPPIC) method to simulate the fluid–solid mixture flows, and an advection–diffusion model for handling the fine contents. The modifications to the MPPIC method include: (i) changing the pure Eulerian fluid model to a hybrid Eulerian–Lagrangian model for numerical flexibility in handling large free-surface deformations, and (ii) replacing the empirical interparticle stress model with the Discrete Element Method (DEM) for numerical stability when dealing with large-size solids. The numerical model is first validated via two physical experiments: (i) wave generation by a granular collapse and (ii) sand dumping from a split hopper. The simulations generally agree well with the experimental findings, reflecting both the fluid–solid interaction and propagation of suspended sediments. Fallpipe rock dumping is then simulated with a consideration of the effects of fallpipe size on the dynamic interactions between the DEM solid particles, the fluid, and, hence, the fine contents. The results show that long narrow fallpipes perform better in terms of containing the fine contents and limiting the spreading range of the DEM solid particles on the seabed. The time-varying distribution of the fines concentration and the fluid velocity within the fallpipe are also discussed based on the simulation results.

Three-dimensional coupling between Boussinesq (FEM) and Navier–Stokes (particle based) models for wave structure interaction

The paper presents coupling between a mesh-based finite-element model for Boussinesq equations (FEBOUSS Agarwal et al., 2022) with a meshless local Petrov–Galerkin model for the Navier–Stokes equations (MLPG_R Agarwal et al., 2021) in 3D. Boussinesq equation models are widely used for simulating wave-propagation over large domains with uneven topography using a 2D surface mesh. Mesh-less models inherently capture large free-surface deformations and have shown promise in simulating wave-structure interaction, run-up and breaking phenomenon. The hybrid approach in this paper assumes a 3D MLPG_R sub-domain surrounded by the 2D mesh of FEBOUSS. The coupling interface in MLPG_R consists of relaxation zones that can be placed along multiple boundaries of the sub-domain for exchanging particle velocity from FEBOUSS. This hybrid model is therefore capable of simulating directional waves, that has not been reported previously.The paper first presents the procedure for calculating the depth-resolved velocities in 3D from the Boussinesq model. The resultant velocities are compared against theory, experiments and other models. The following sections present the coupling algorithm along a single and multiple coupling interfaces in MLPG_R. Validation results for this hybrid model are provided using surface elevation and velocity measurements for regular waves, including directional cases. In general, the results from the hybrid model are reported to have marginal over-prediction of peaks compared to purely MLPG_R simulation. Finally, the interaction of a vertical cylinder with direction regular wave is simulated using the 3D hybrid model.

Application of normalized SPH method to inviscid fluid flows with large deformation of free surface

A new normalized smoothed particle hydrodynamics (SPH) method has been presented recently and applied to transient solid mechanics problems of small deformation. The method can overcome boundary deficiency of the conventional SPH method without troublesome inversion of corrective matrix and provide convenience for treating boundary conditions. In this paper, a formulation of the normalized SPH method is derived for modeling inviscid fluid flows with large deformation of free surface. The treatment of dynamic free surface boundary conditions in the present method is addressed and theoretically compared with that in the conventional SPH method. A method based on kernel estimation is proposed for calculation of boundary summation and compared with the method based on α-shape. The normalized SPH method is applied to modeling inviscid free surface flows. Numerical results demonstrate that the present method is capable of modeling large deformation of free surface and can produce higher accuracy than the conventional SPH method, especially at boundary regions. The newly developed kernel estimation method for the calculation of boundary summation is more efficient than the α-shape-based method, and makes the computational efficiency of the normalized SPH method close to the conventional SPH method. To simulate violent free surface flows, a particle shifting technique is introduced in the present method. With this technique, the method is applied to simulating extremely large deformation, fragmentation and reconnection of free surface.

A numerical study on sloshing mitigation by vertical floating rigid baffle

Due to large hydrodynamic loads generated by the violent free surface flow, sloshing in partially filled tanks is an important phenomenon for the design of several offshore structures such as FPSO platforms, LNG carriers, crude oil carriers and, more recently, FLNGs. This study is focused on the numerical investigation of sloshing mitigation devices based on a floating baffle. For this purpose, the complex and highly nonlinear sloshing phenomenon is modeled and simulated using the Moving Particles Semi-Implicit (MPS) method, which is a fully-Lagrangian particle-based method for the simulation of incompressible flows widely applied to the study of fluid–structure interaction phenomena involving large free surface deformations, fragmentation and merging. As a reference for an in-depth discussion, the effectiveness of the equivalent fixed baffles placed at the bottom, the ceiling and mid-height of the tank were also studied. This work is divided into three parts: (1) the validation of the numerical method, (2) the study on the effect on sloshing of fixed baffles placed amid-tank and at different heights and (3) the investigation of the sloshing mitigation performance of floating baffles with a degree of freedom in the vertical direction of the tank. The effects of the floating baffles densities, which influence the draft of the baffles, on sloshing are investigated as well. The use of fixed baffles provided effective sloshing mitigation at the resonant frequencies for certain filling conditions depending upon the location of the baffle, but it might lead to even more violent flows in other filling conditions. On the other hand, the floating device presented sloshing mitigation for a larger range of filling conditions. Moreover, four different patterns of resonant motion of the floating baffle were identified and simple analytical estimations that could predict corresponding natural frequencies were proposed herein.

SPH modeling of caisson stability on rubble-mound foundation under wave action

<p indent="0mm">The caisson breakwater is the representative protective structure in coastal and offshore zones, which is mainly composed of the reinforced concrete caisson and the rubble-mound foundation. The displacement and inclination of caisson structures are generally considered to be the typical features of the failure of the composite breakwaters. Therefore, understanding the motion response characteristics of caisson structures under wave action is of great importance for the design and the safe operation of caisson breakwaters. The dynamic response of caisson breakwaters under wave action is very complex, due to the interaction between wave-porous media-solid structures. In order to predict the stability of caisson breakwaters numerically, the complex free surface flow and the porous flow in the permeable foundation, as well as the contact interaction between the permeable foundation and the caisson structure should be accurately described. The existing numerical research for wave interaction with caisson breakwaters is usually assumed that the caisson structure is fixed in space, and the main interests focus on the wave deformation, the wave load acting on the caisson structure as well as the velocity and pressure fields in the vicinity of the composite breakwater. Few studies pay attention to the motion response and the instability of caisson structures. In addition, the traditional grid-based numerical models are commonly introduced to model wave interaction with the composite caisson breakwaters. These models, although powerful, may have difficulty dealing with extremely large deformation problems and usually also require an explicit surface capturing scheme. In comparison, the mesh-free smoothed particle hydrodynamics(SPH) method does not require the explicit surface capturing scheme in treating strong nonlinear flows with large free surface deformation and enables the easy modeling of coastal structures with complex geometrical boundaries. In this paper, based on the previously established SPH porous flow model, a contact interface boundary condition is developed between the permeable foundation and the upper caisson structure by modeling the supporting force and the sliding friction force at the interface boundary, and a new SPH model is established to study the caisson stability on the permeable foundation under wave action. Compared with the corresponding experimental data, it is found that the developed SPH model can reasonably predict the horizontal wave load, the vertical lift force acting on the caisson structure, and the motion response of the caisson structure. Compared with the other numerical model, it is found that the motion responses of the caisson structure predicted by the present SPH model have a better agreement with the experimental data. All the results indicate that the developed SPH model can be used as a robust tool to predict the stability of caisson breakwaters. However, it is undeniable that the predicted motion response of the caisson structure still deviates from the corresponding experimental data slightly. The main reason is that the contact interface boundary condition between the caisson structure and the permeable foundation ignores the deformation of the contact surface and the adjustment of the stress distribution, which is caused by the embedded effect of the caisson toe and the stone dislocation of the rubble-mound foundation.

Mechanism study on spreading dynamics of nanofluids droplet coupled with thermal evaporation

Droplet-wall interactions occur in many advanced engineering technologies, such as 3D printing, spray coating, and even quantum light-emitting diode(QLED). Nanofluids (colloids of nanoparticles) are becoming increasingly important working fluids for more excellent performances. Computer modeling of fluid flows with the large deformation of free surface usually presents great challenges for conventional grid-based numerical methods. The smoothed particle hydrodynamics (SPH) method has been widely used in such droplet dynamics because of its meshless Lagrange methods, as well as the applicability to macro-scale simulation. In the paper, the numerical model based on the SPH method is presented to predict the detailed outcome of sessile and transient nanofluid droplets. The surface tension of droplets is taken into consideration by the inter-particle interaction force (IIF) model for its advantages in modeling the contact angle during wetting. The properties of nanofluids are obtained by averaging the properties of base fluids and nanoparticles, based on the assumption that nanofluids of low concentration are a homogeneous mixture and Newtonian fluid. The assumption is proposed based on the rheological measurement of nanofluids. Heat conduction is added into the SPH model when the impacted surfaces are heated, and the evaporation is modeled by “extinguishing” the SPH particles. The SPH model predicts the evolution of the droplet surface from spreading to receding, even rebounding on the wall. Moreover, the normalized droplet diameters predicted by the SPH model agree well with the experimental data from the high-speed camera. The proposed SPH models have been used to study the effects of heating temperatures and nanofluids concentration on droplet-wall interactions. The modified SPH models can handle the nanofluids droplet dynamics, along with large deformation, thermal transfer, and evaporation. The results demonstrate that the SPH model is a powerful tool to study the complex droplet dynamics and to predict the patterns of droplet deformation as well as the thermal distribution.

SPH–FV coupling algorithm for solving multi-scale three-dimensional free-surface flows

In two previous papers we presented an algorithm for coupling the Finite Volume (FV) method for the solution of 2D Navier–Stokes equations discretized on block structured Eulerian grids with the weakly-compressible Lagrangian Smoothed Particle Hydrodynamics (SPH) method. This coupling procedure exploits the SPH method to discretize flow regions close to free-surfaces and the Finite Volume approach to resolve both the bulk flow and the wall regions, where grid stretching can be favourably used. The information exchange between the two numerical schemes is established through overlapping zones. In the present paper this coupling paradigm is extended to a 3D framework. To this purpose, the extension of the algorithms for particle creation/deletion on the interfaces are described and issues related to free-surface intersection with each sub-domain boundary are addressed. Moreover, a new coupling procedure that simplifies the algorithm is proposed and tested. Effectiveness and accuracy achieved by the coupled solver are tested on challenging problems involving large free surface deformations and vorticity generation like the 3D flow past a cylinder below a free surface, the breaking wave generated by a ship bow in forward motion and the impact of a flat plate on the water surface.

MODELING COMPLEX FLOW INDUCED BY WATER WAVES PROPAGATION OVER SUBMERGED SQUARE OBSTACLES

Submerged breakwaters are efficient structures used for shore protection. Many design features of these structures are captured upon modeling wave propagation over submerged square obstacles. The presence of separation vortices and large free surface deformations complicates the problem. A multiphase turbulent numerical model is developed using ANSYS commercial package. Careful domain discretization is done employing suitable mesh clustering to capture high gradients. Various numerical model parameters are provided, including grid size and time step. Special attention is directed towards clarifying turbulence initial conditions. Stable simulation results are obtained within acceptable computational time. Numerical results are validated quantitatively using subsurface measurements. Comparison along continuous horizontal and vertical velocity profiles is provided. Temporal and spatial model resolutions are illustrated for three test cases. The effect of wave period and height is well focused. The unsteady vortical structure is visualized. The incident wave energy is calculated and validated against theoretical values. The wave energy dissipation characteristics are briefly explained.

Updated Lagrangian particle hydrodynamics (ULPH) modeling of solid object water entry problems

Solid object water entry is a common problem in various natural, industrial and military applications, which involves large deformation of free surfaces and violent fluid–structure interactions. In computational fluid dynamics (CFD), this is a type of problem that tests the robustness and capacity of any CFD numerical algorithm. In this work, the newly-developed updated Lagrangian particle hydrodynamics (ULPH) method, which is a fluid version of peridynamics, is enhanced and applied to simulate solid object water entry problems. ULPH method is Lagrangian meshfree particle method that can ensure the specific free surface conditions automatically satisfied. The density filter and artificial viscosity diffusion are adopted in the ULPH scheme to stabilize and smooth the pressure field. In the process of a rigid body entering water, it may induce negative pressure in some areas of impact region, which can cause spurious tensile instability in some meshfree particle simulations, such as SPH and ULPH. A tensile instability control technique based on the ULPH framework has been developed to overcome the numerical instability. To validate the stability and accuracy of the ULPH approach in simulating water entry problems, several 2D and 3D examples of water entry have been carried out in this work. The necking and cavity pinch-off phenomena are visible in the numerical results. The simulation results of the ULPH method are well compared with experimental data and other numerical solutions. The water crown, cavity shapes and stream pattern formed around the rigid body entering the water can be well captured. The computation results show that the ULPH method has the ability to simulate the complex solid object water entry precess accurately.

Simulating focused wave impacts on point absorber wave energy converters

This study contributes to the Collaborative Computational Project in Wave–Structure Interaction blind test series 2 by numerically investigating the dynamic response of two simplified point absorber wave energy converters (WECs – a hemispherical-bottom cylinder and a cylinder with moon-pool) under the action of focused waves of varying steepness. The open source toolbox OpenFOAM along with its new overset grid functionality is applied and evaluated for the complex flow problem involving both large free surface deformations and large-amplitude motions of floating objects. The quality of the numerically generated focused wave groups is first examined and validated against the experimental data. The effects of both wave steepness and the moon-pool on the dynamic responses and mooring loads of the simplified WECs are then analysed.

A Comparison Between Weakly-Compressible Smoothed Particle Hydrodynamics (WCSPH) and Moving Particle Semi-Implicit (MPS) Methods for 3D Dam-Break Flows

Lagrangian particle-based methods have opened new perspectives for the investigation of complex problems with large free-surface deformation. Some well-known particle-based methods adopted to solve non-linear hydrodynamics problems are the smoothed parti- cle hydrodynamics (SPH) and the moving particle semi-implicit (MPS). Both methods model the continuum by a system of Lagrangian particles (points), but adopting distinct approaches for the numerical operators, pressure calculation, and boundary conditions. Despite the ability of the particle-based methods in modeling highly nonlinear hydrodynamics, some shortcomings, such as unstable pressure computation and high computational cost remain. In order to assess the performance of these two methods, the weakly-compressible SPH (WCSPH) parallel solver, DualSPHysics, and an in-house incompressible MPS solver are adopted in this work. Two test cases consisting of three-dimensional (3D) dam-break problems are simulated, and wave heights, pressures and forces are compared with the available experimental data. The influence of the artificial viscosity on the accuracy of WCSPH is investigated. Computational times of both solvers are also compared. Finally, the relative benefits of the methods for solving free-surface problems are discussed, therefore providing directions of their applicability.

Ship hull slamming analysis with smoothed particle hydrodynamics method

In the marine and ocean engineering area, the water-entry process is a typical problem of fluid-solid interaction, which involves complex phenomenon such as the large deformation of free surface and considerable structure movement. In this process, the predicting impact load and summarizing the evolution law of the free surface deformation have important reference significance for the hull structure design. To address this issue, numerical simulations are carried out using a robust Smoothed Particle Hydrodynamics (SPH) model. The accuracy of the present SPH model is firstly validated by simulating the water entry of bow-flare section in two and three dimensions, respectively. Then, we investigate the variation characteristics of impact load and the evolution of free surface during the entry of the bow-flare ship section with different roll angles (θ=0∘∼20.3∘). Attention is focused on the flow separating phenomenon and the spray jet on the free surface. Finally, the water entry of a three dimensional ship hull is simulated. The velocity and pressure of flow field are analyzed and some conclusions are drawn.

Moving surface mesh-incorporated particle method for numerical simulation of a liquid droplet

In this study, a new particle method for simulating the dynamics of a liquid droplet in a two-dimensional space has been developed. The proposed method incorporates a moving surface mesh to represent a deformable free-surface boundary. The domain enclosed by the surface mesh is defined as a liquid volume (droplet), and the outer region is a gas phase with constant pressure. Fluid particles are seeded inside the liquid domain, and also, discrete nodes along the surface mesh are defined as additional computational points. The incompressible flow is solved based on the LSMPS (least squares moving particle semi-implicit) method, where all differential operators are discretized by means of consistent schemes. The stress balance equations are solved along free surfaces, where the surface tension force is directly evaluated by the geometry of the surface mesh at each surface node. As numerical tests, various problems including a hydrostatic pressure problem, circular and square patch tests, droplet oscillations and static droplets suspended by solid walls have been simulated. As a result, the proposed method shows excellent agreement with the reference solutions, even under large free-surface deformations, which verifies the validity of the current developments.

A 3D parallel particle-in-cell solver for extreme wave interaction with floating bodies

Floating structures are widely used for vessels, offshore platforms, and recently considered for deep water floating offshore wind system and wave energy devices. However, modelling complex wave interactions with floating structures, particularly under extreme conditions, remains an important challenge. Following the three-dimensional (3D) parallel particle-in-cell (PIC) model developed for simulating wave interaction with fixed bodies, this paper further extends the methodology and develops a new 3D parallel PIC model for applications to floating bodies. The PIC model uses both Lagrangian particles and Eulerian grid to solve the incompressible Navier-Stokes equations, attempting to combine both the Lagrangian flexibility for handling large free-surface deformations and Eulerian efficiency in terms of CPU cost. The wave-structure interaction is resolved via inclusion of a Cartesian cut cell method based two-way strong fluid-solid coupling algorithm that is both stable and efficient. The numerical model is validated against 3D experiments of focused wave interaction with a floating moored buoy. Good agreement between the numerical and experimental results has been achieved for the motion of the buoy and the mooring force. Additionally, the PIC model achieves a CPU efficiency of the same magnitude as that of the state-of-the-art OpenFOAM® model for an extreme wave-structure interaction scenario.

Numerical Simulation of Stirred Vessels and the Devolatilization Process Using the Particle Method with Bubble Model

A stirred vessel is a device for mixing fluids. It is widely-used in industry and plays an important role in the chemical process. In the stirred vessels, liquid is stirred by the rotational motion of impeller, and often, there exists large deformation of free surface. The moving particle semi-implicit (MPS) method is a meshfree particle method suitable for such complex physical phenomena because moving boundaries can be handled with relative ease. The devolatilization process is one of the applications of stirred vessel, where dissolved volatile components are removed by inducing the nucleation of bubbles in the tank. This paper explains numerical algorithms for the stirred vessel analysis with the MPS method. Furthermore, numerical simulations of the devolatilization process using the MPS method with incorporated bubble models are presented.

Numerical modeling of floating bodies transport for flooding analysis in nuclear reactor building

Abstract The nuclear reactor safety analysis especially related to flooding accidents becomes more and more important after the Fukushima nuclear accident. In case of an internal or external flooding accident, some large floating bodies, such as broken doors, emergency powers or even parked vehicles, could cause severe damage and serious problems, requiring the transport studies of moving solids during flooding accidents. The Explicit Moving Particle Simulation (EMPS) method is one of the particle methods, in which large deformation of free surfaces and Lagrangian interfaces can be easily tracked and simulated. Due to its high computational efficiency and easy applicability of the large scale and massively parallel computing, the EMPS method is employed to reproduce the transport of rigid body in free surface flows in this study. The solid-fluid interaction is based on the Passively Moving Solid (PMS) model, while the solid-solid interactions are represented by the discrete element method (DEM). A coupled algorithm, applying different time steps for EMPS and DEM, is proposed in this study. In order to validate this method, several numerical tests are carried out. A wooden block rising from a water tank is simulated to validate the PMS model while the cylinders collapse is calculated to test DEM. Then the freely falling solid body movements with different damping coefficients are simulated to verify the coupled algorithm. Afterward, a 3D dam break flow involving fixed obstacles and a transportable floating body is studied. The histories of water depths and floating bodies’ movements are compared with experimental observations. Additionally, another complex 3D dam break event involving multiple floating bodies is simulated for further validation. The trajectories of bodies are investigated, and sensitivity study of the damping coefficient is preliminarily conducted. Finally, in order to demonstrate the capability of the present method, an internal flooding accident with floating bodies transport in AP1000 is presented as an example.

A 3D parallel Particle-In-Cell solver for wave interaction with vertical cylinders

In this paper, the Particle-In-Cell (PIC) based PICIN solver is extended to three spatial dimensions and parallelised using the Message Passing Interface (MPI) approach. The PICIN solver employs both Eulerian grid and Lagrangian particles to solve the incompressible Navier-Stokes equations for free-surface flows. The particles are employed to carry all the fluid properties, solve the non-linear advection term and track the free-surface, while the grid is used solely for computational efficiency in solving the non-advection terms. Validation of the new 3D model concentrates on test cases involving multiple wave types (including regular waves, focused waves and solitary waves) interacting with vertical cylinders in several spatial configurations. The results are compared with laboratory data and numerical results from state-of-the-art Volume of Fluid (VOF) based Eulerian solvers such as those from the OpenFOAM® suite. It is shown that the 3D parallel PICIN model is able to well simulate highly non-linear water waves, and the interaction of such waves with vertical cylinders, with a CPU efficiency similar to Eulerian solvers. Moreover, the innovative use of particles in PICIN, akin to meshless Lagrangian solvers, gives the model a particular flexibility in handling complex, full 3D, water-wave scenarios involving large free-surface deformations.

Numerical modeling of flood waves in a bumpy channel with the different boundary conditions

In this paper, the Incompressible Smoothed Particle Hydrodynamics (ISPH) method is presented to simulate flood waves in uneven beds. The SPH method is a mesh free particle modeling approach that is capable of tracking the large deformation of free surfaces in an easy and accurate manner. Wave breaking is one of the phenomena that its free surface is complicated. Therefore, ISPH method is robust tool for the modeling of this kind of free surface. The basic equations are the incompressible mass conservation and Navier–Stokes equations that are solved using a two-step fractional method. In the first step, these equations are solved to compute velocity components by omitting the pressure term and in the absence of incompressible condition. In the second step, the continuity constraint is satisfied and the Poisson equation is solved to calculate pressure terms. In the present model, a new technique is applied to allocate density of the particles for the calculations. By employing this technique, ISPH method is stabled. The validation by comparison with laboratory data is conducted for bumpy channel with various boundary conditions. The numerical results showed good agreement with available experimental data. Also relative error is calculated for two numerical cases.

Challenges on the numerical prediction of slamming loads on LNG tank insulation panels

The load assessment in water impacts problems involving complex geometries is generally a quite challenging task for numerical solvers. Indeed, the occurrence of large free-surface deformation, air cushioning and possible compressibility effects strain the standard Computational Fluid Dynamics (CFD) codes to their limits. In the present work, an enhanced Smoothed Particle Hydrodynamics (SPH) model is adopted to evaluate the pressures acting on the surface of smooth and corrugated panels impacting water and the numerical outcomes are compared to experimental data and analytical solutions. Specifically, the water entry of a flat panel at 4° is firstly studied in order to highlight the main critical aspects underlying the numerical solution of water impacts with small deadrise angles. Then, the water impact of a Mark III type panel (a corrugated insulation panel) adopted in LNG tanks is considered. Experimental data involving wet drop tests of both flat and corrugated panels have been performed and the pressures during the impact have been measured at several points along the panel surface. Complex features of the flow, such as 3D effects and air-cushioning, have been addressed by a developing the numerical study in steps of increasing complexity.

Experimental study on large deformation of free surface during water exit of a sphere

During water exit of a solid body, the free surface is disturbed and deformed. To study the free-surface deformation and its dynamic change such as breakup, a set of water-exit equipment was designed and a series of experiment on water exit of a sphere were conducted. High-speed photographic technologies were adopted to capture the whole process of water exit and the large deformation of the free surface. Work was divided into forced water exit and free water exit. In the forced water exit, either a fully-submerged or a partially-submerged sphere was pushed out of water at a constant speed. The influence of the velocity or Froude number was investigated. In the free water exit, an initially static sphere with an equivalent density smaller than water was released underwater by using an electromagnet. Water exit at different initial submergence depth was conducted. Velocity and acceleration of the light sphere are analysed.